Benchmarks in Tokyo, Shanghai and Hong Kong declined. Seoul and Sydney were little-changed.
Investors were encouraged by the announcement that top U.S. and Chinese negotiators, Trade Representative Robert Lighthizer and Vice Premier Liu He, talked Monday by phone. No details were released.
The conflict over Beijing's technology ambitions and trade surplus was weighed on global trade and fed fears it will depress global growth. Tensions have worsened after Washington tightened sanctions on Chinese tech giant Huawei.
"Both presidents have a very low bar of merely agreeing to resume trade talks, without having to iron out any of the sticking points at the G20," said Chang Wei Liang of Mizuho Bank in a report.
The realities of achieving a settlement "will probably be relegated to the backseat as the 'feel good' factor of the G20 displaces caution," Chang said.
The Shanghai Composite Index lost 1.1% to 2,974.69 and Tokyo's Nikkei 225 shed 0.2% to 21,241.28. Hong Kong's Hang Seng retreated 0.9% to 28,268.14.
Seoul's Kospi added one point to 2,128.00 while Sydney's S&P-ASX 200 gained three points to 6,667.40. Taiwan also declined while markets in Southeast Asia and New Zealand advanced.
On Wall Street, smaller company stocks had their worst day since May, helping to erase some of last week's gains after the benchmark Standard & Poor's 500 index closed at an all-time high.
The S&P 500 index slipped 0.2% to 2,945.35. The Dow Jones Industrial Average rose less than 0.1% to 26,727.54. The Nasdaq composite dropped 0.3% to 8,005.70.
The Russell 2000 index of smaller companies slid 1.3% to 1,530.08, its biggest single-day loss since May 31.
Investors have been reassured by statements from the Federal Reserve this month that suggest the central bank is prepared to cut interest rates in response to a slowing global economy. Even so, traders remain concerned that corporate profits might suffer should the kind of economic slowdown that would prompt the Fed to cut rates take hold.
The U.S.-Chinese standoff was triggered by complaints Beijing steals or pressures companies to hand over technology.
Lighthizer and Liu wrapped up their latest round of talks in May with no date to meet again. China laid out conditions for a settlement in early June, saying it must be "balanced," reflecting complaints Washington is pushing for a one-sided deal and to retain punitive tariffs on Chinese goods.
ENERGY: Benchmark U.S. crude fell 50 cents to $57.40 per barrel in electronic trading on the New York Mercantile Exchange. The contract gained 47 cents on Monday to close at $57.90. Brent crude, used to price international oils, lost 51 cents to $63.67 per barrel in London. It shed 27 cents the previous session to $64.18.
CURRENCY: The dollar declined to 107.05 yen from Monday's 107.29 yen. The euro edged up to $1.1403 from $1.1400.